Summary
In this note we present examples of projective spectraɛ=(E n ) n ∈ℕ of (LB)-spaces satisfying proj1 ε≠0 such that the inductive spectrum (E n ′) n ∈ℕ of the duals is strict. Moreover, we characterize proj1ε=0 for projective spectra of Moscatelli type.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Braun, R. W.: The surjectivity of a constant coefficient differential operator on the real analytic functions and the geometry of its symbol. Ann. Inst. Fourier, to appear
Braun, R.W., Meise, R., Vogt, D.: Applications of the projective limit functor to convolutions and partial differential equations. Advances in the theory of Fréchet spaces, NATO ASF series C287 (Ed. T. Terzioĝlu), Dordrecht: Kluwer (1989)
Braun, R.W., Meise, R., Vogt, D.: Existence of fundamental solutions and surjectivity of convolution operators on classes of ultradifferentiable functions. Proc. London Math. Soc.61, 344–370 (1990)
Braun, R.W., Meise, R., Vogt, D.: Characterization of the linear partial differential operators with constant coefficients which are surjective on non-quasianalytic classes of Roumieu type on ℝN. Math. Nachr.168, 19–54 (1994)
Dierolf, S., Domański, P.: Factorization of Montel operators. Studia Math.107, 15–32 (1993)
Frerick, L.: On vector valued sequence spaces. Note di Matematica, to appear
Moscatelli, V.B.: Fréchet spaces without continuous norms and without bases. Bull. London Math. Soc.12, 63–66 (1980)
Müller, S., Dierolf, S., Frerick, L. On acyclic inductive sequences of locally convex spaces, Proc. R. Ir. Acad.94, 153–159 (1994)
Palamodov, V.P.: The projective limit functor in the category of linear topological spaces (Russian). Mat. Sb.75, 567–603 (1968), English trans Math. USSR-Sb4, 529–558 (1968)
Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces. North-Holland Math. Studies131 (1987)
Retakh. V.S.: Subspaces of a countable inductive limit. (Russian), Dokl. Akad. Nauk SSSR194 (1970), English transl. Soviet Math. Dokl.11, 1384–1386 (1970)
Vogt, D.: Lectures on projective spectra of (DF)-spaces. Seminar lectures, AG Funktionalanalysis Düsseldorf/Wuppertal (1987)
Vogt, D.: Topics on projective spectra of (LB)-spaces. Advances in the theory of Fréchet spaces, NATO ASF series C287 (Ed. T. Terzioĝlu), Dordrecht, Kluwer (1989)
Vogt, D.: Regularity properties of (LF)-spaces. Progress in Functional Analysis (Eds. K. D. Bierstedt, J. Bonet, J. Horvath, M. Maestre) North-Holland Math. Studies170 (1992)
Author information
Authors and Affiliations
Additional information
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag
Rights and permissions
About this article
Cite this article
Dierolf, S., Frerick, L., Mangino, E. et al. Examples on projective spectra of (LB)-spaces. Manuscripta Math 88, 171–175 (1995). https://doi.org/10.1007/BF02567814
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02567814